The third season of Toaru Kagaku no Railgun started and Accelerator, one of the main villains of Toaru Majutsu no Index and the main character of Toaru Kagaku no Accelerator appears in the first episode. How is this series placed in the timeline then? Does Toaru Kagaku no Railgun season 3 happens after or before the events of Toaru Kagaku no Accelerator?

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The Accelerator anime covers the Necromancer Arc, which (in-universe) starts in early September and ends sometime before September 14.

The Railgun T anime covers the Daihaisei Festival Arc (Railgun version), which (in-universe) starts on September 19 and ends on September 20. It might also cover the Dream Ranker Arc after that, which (in-universe) starts on September 26 and ends sometime in mid-October.

Index, Railgun, and Accelerator pretty much all take place within the same year (not counting flashbacks), but as readers/watchers, we're not sure which year it is (it's never specified directly). See the footnote on the Unified Story Timeline#Trivia page on the Toaru Wikia for more information.

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    @Pablo Yes, it's all in the same year. In the Toaru verse, a lot happens over a really short period of time. For example, over the course of 22 Index novels and 23 NT Index novels, less than 5 months have elapsed in-universe. It's unknown which year it is, though. It's known from the novel side stories that whatever year this is, March 15 is the third Friday of March, and also there are five Fridays in September. Which apparently is impossible by our current calendar. So ¯\_(ツ)_/¯
    – ahiijny
    Commented Jan 15, 2020 at 15:11

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